Determination of the optimum steady-state performance of an open-loop and a closed-loop valve-controlled hydro-motor drive: a design approach

  • Sujit Kumar
  • K. Dasgupta
  • J. Das
Technical Paper


This article analyses the steady-state performance of an open-loop and a closed-loop proportional valve-controlled hydro-motor drive. The drives considered for the analysis consist of HSLT and LSHT hydro-motors. In this respect, considering the flow and torque losses of the valve and the hydro-motors, the system equations are deduced from the model. They are made non-dimensionalised, from where the expressions of the performance parameters in terms of the speed, efficiency and power transfer of the drives are determined. From the explicit design equations, the conditions for the maximum efficiency and the power transfer are obtained. The drives performances are analysed in both open-loop and closed-loop configurations and compared with the test data. Using the explicit design equations developed from the model, the effects of the losses of the hydro-motors and the control gain on the performance of the drives are studied. Using the simplified set of design equations developed in the model, the drive’s performance can be determined within its reasonable operating zone from a limited amount of test data.


Steady state Proportional valve Open loop Closed loop Flow losses High-speed, low-torque (HSLT) hydro-motor Low-speed, high-torque (LSHT) hydro-motor 

List of Symbols


Energy storage capacitive element used in bond graph model


Constant in flow equations


Closed-loop gain


Discharge coefficient of the proportional valve


Proportional amplifier gain


Speed sensor gain


Input voltage signal to the Proportional valve


Proportional flow constant


Generalised speed of the hydro-motor speed (rpm)


No-load motor speed (rpm)

\(\overline{N}_{mp}\), \(\overline{N}_{ma}\)

Non-dimensional predicted and actual speed, respectively

Pl, \(\overline{P}_{l}\)

Load pressure (bar) and its non-dimensional value


Supply pressure (bar)


Sump pressure (bar)

P1, P2, \(\overline{P}_{1}\), \(\overline{P}_{2}\)

Line pressures (bar) and its non-dimensional values


Cross port leakage of the proportional valve (lpm)


Mean flow rate (lpm)

Q1, Q2, \(\overline{Q}_{1}\), \(\overline{Q}_{2}\)

Line flow rates (lpm) and its non-dimensional values


Energy dissipative element used in bond graph model


Hydro-motor cross port leakage coefficient (Ns/m5)


Cross port leakage resistance of the proportional valve (Ns/m5)


Hydro-motor external leakage coefficient (Ns/m5)


Equivalent leakage resistance of hydro-motor (Ns/m5)


Line resistance (Ns/m5)


Source of effort element used in bond graph model


Source of flow element used in bond graph model


Multi-port element that transforms mechanical to hydraulic power and vice versa used in bond graph model


Load torque (N m)

Tls, \(\overline{T}_{ls}\)

Torque loss (N m) and its non-dimensional value


Displacement of hydro-motor (cc/rev)

\(\overline{W}_{mp}\), \(\overline{W}_{ma}\)

Non-dimensional predicted and actual Power transfer to motor, respectively


Motor flow coefficient


Internal flow loss coefficient of the proportional valve


External flow loss coefficient of the hydro-motor

ηmp, ηma

Predicted and actual efficiency of the hydro-motor drive, respectively.


Common flow bond graphic junction


Common effort bond graphic junction


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mining Machinery EngineeringIndian Institute of Technology (Indian School of Mines)DhanbadIndia

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